This guide aims to provide an effective strategy for achieving victory in the Shark Game within the game DAVE THE DIVER.
Summary
To summarize the strategy briefly, you should select a number equal to the remainder obtained by subtracting 1 from the cavity number and dividing the result by 4. If the remainder is 0, aim to reach 4 as the next number. When you choose a number resulting in 4n+remainder, where n represents any number (including 0), you have already won. Simply select 4 minus your opponent’s number, and witness the magical outcome.
Explanation of the Strategy
The shark tooth game adheres to the principles of the “100 Game” developed by Reverend Charles Lutwidge Dodgson, better known as Lewis Carroll, the author of Alice in Wonderland. While the “100 Game” involves selecting numbers from 1 to 10, the shark tooth game limits the range to numbers 1 to 3. I will provide a concise explanation of the strategy and elaborate on the underlying theory. By following this approach, you can always secure a victory in this game.
Establishing the Plan
First, identify the cavity, which is self-evident. Since the bottom row contains 20 teeth, you can determine your target based on its position from left to right. Let’s assume the tooth number is 18 for the purpose of illustration.
Calculate the remainder (or modulus) by dividing the target number minus 1 by 4, while also keeping the quotient in mind. For example, for a target number of 18, the calculation (18-1)/4 yields a quotient of 4 and a remainder of 1. Both the remainder and quotient are significant.
Irrespective of your opponent’s selection, you can always choose an option that leads to a sum of 4. In other words, subtract your opponent’s number from 4 to determine your own number. If your opponent chooses 1, you select 3; if they choose 2, you choose 2; and if they choose 3, you choose 1. This strategy grants you control over the game’s progression while ensuring that you consistently obtain the subsequent number in the sequence.
Unlike the “100 Game,” your objective is to make your opponent reach the target number, rather than reaching it yourself. This explains why we subtracted 1 from the target number. Our aim is to ensure that we reach the target number minus one, so that when it’s the opponent’s turn after ours, they must hit the target number and consequently lose.
Playing the Game
Initially, select the remainder as an option. In our example, the remainder is 1. Subsequently, the opponent will choose a number. As previously explained, subtract their chosen number from 4 to obtain your own number. Respond with 3 if they select 1, 2 if they choose 2, and 1 if they pick 3. For our target number of 18, the sequence progresses as follows (with bold representing the range of the opponent’s possible choices):
1, 2-4, 5, 6-8, 9, 10-12, 13, 14-16, 17. As you pass the turn at 17, any number chosen by the opponent will result in reaching the target number, thereby leading to your victory.
The Exception
The exception to this strategy occurs when the remainder is 0. Since selecting 0 is not feasible, what should be done in such a scenario? Let’s consider the target number 17 and explore the situation similarly to the previous example: (17-1)/4 yields a quotient of 4 and a remainder of 0.
The advantage lies in the fact that the opponent does not adopt the same optimal play as we do. They are likely to make mistakes. In this new scenario, our objective is to choose a number that brings us to a multiple of 4 as early as possible, ensuring that we select 16, leaving the opponent with the choice of 17.
If the remainder is 0, aim to reach a multiple of 4. Starting with 1 places you farther from the desirable number, 16. If the opponent selects 1 or 2, you are in a favorable position. Choose the number that brings the sum to 4, thus setting the stage for an easy victory. Even if the opponent selects 3 in response to your choice of 1, all hope is not lost. You have several rounds to get lucky. Simply continue selecting 1 and wait until they do not choose 3.
However, one might wonder about the scenario where you are unfortunate enough to reach a point where the sum is at 12 and it’s your turn to choose. Opting for 3 and bringing the total to 15, in the hope that the opponent selects 2 or 3, holds the same realistic odds as if they were to select 1 or 2 in response to your choice of 1, allowing you to reach a winning position. If they choose 3 in response to your 1, you are at a disadvantage. The odds remain the same, so it is not a suboptimal choice, but it does complicate the strategy. Similarly, selecting 2 places the opponent in a situation where they lose if they choose 2, you win if they choose 1, and you win when they reach 17. The odds remain at 2 to 1 in your favor.
Ultimately, if you cannot maneuver into a winning position (4n+remainder, for the math enthusiasts), you are still reliant on the opponent choosing a number that does not result in a multiple of 4. This allows you to subsequently reach a multiple of 4. Although selecting a larger number may expedite the game by a few seconds, it does not impact the odds unless you are being prevented from selecting the number 4, which occurs when the opponent chooses 1. The rounds are never skipped unless suboptimal play is involved. The odds remain constant.
That's everything we are sharing today for this DAVE THE DIVER guide. This guide was originally created and written by Zak Light. In case we fail to update this guide, you can find the latest update by following this link.